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Spectral Geometry of Shapes

Spectral Geometry of Shapes
  • Author : Jing Hua,Zichun Zhong
  • Publisher :Unknown
  • Release Date :2020-01-15
  • Total pages :195
  • ISBN : 9780128138427
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Summary : Spectral Geometry of Shapes presents unique shape analysis approaches based on shape spectrum in differential geometry. It provides insights on how to develop geometry-based methods for 3D shape analysis. The book is an ideal learning resource for graduate students and researchers in computer science, computer engineering and applied mathematics who have an interest in 3D shape analysis, shape motion analysis, image analysis, medical image analysis, computer vision and computer graphics. Due to the rapid advancement of 3D acquisition technologies there has been a big increase in 3D shape data that requires a variety of shape analysis methods, hence the need for this comprehensive resource. Presents the latest advances in spectral geometric processing for 3D shape analysis applications, such as shape classification, shape matching, medical imaging, etc. Provides intuitive links between fundamental geometric theories and real-world applications, thus bridging the gap between theory and practice Describes new theoretical breakthroughs in applying spectral methods for non-isometric motion analysis Gives insights for developing spectral geometry-based approaches for 3D shape analysis and deep learning of shape geometry

Shape Optimization and Spectral Theory

Shape Optimization and Spectral Theory
  • Author : Antoine Henrot
  • Publisher :Unknown
  • Release Date :2017-05-08
  • Total pages :474
  • ISBN : 3110550857
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Summary : "Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization. It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results. Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Antunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noel Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartlomiej A., Velichkov Bozhidar

Old and New Aspects in Spectral Geometry

Old and New Aspects in Spectral Geometry
  • Author : M.-E. Craioveanu,Mircea Puta,Themistocles RASSIAS
  • Publisher :Unknown
  • Release Date :2013-03-14
  • Total pages :446
  • ISBN : 9789401724753
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Summary : It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.

Spectral Geometric Methods for Deformable 3D Shape Retrieval

Spectral Geometric Methods for Deformable 3D Shape Retrieval
  • Author : Chunyuan Li
  • Publisher :Unknown
  • Release Date :2013
  • Total pages :229
  • ISBN : OCLC:1032921560
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Summary :

Steklov Geometry Processing

Steklov Geometry Processing
  • Author : Wang Yu (S.M.)
  • Publisher :Unknown
  • Release Date :2018
  • Total pages :80
  • ISBN : OCLC:1051458896
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Summary : We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.

Numerical Geometry of Non-Rigid Shapes

Numerical Geometry of Non-Rigid Shapes
  • Author : Alexander M. Bronstein,Michael M. Bronstein,Ron Kimmel
  • Publisher :Unknown
  • Release Date :2008-09-18
  • Total pages :346
  • ISBN : 0387733019
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Summary : Deformable objects are ubiquitous in the world surrounding us, on all levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. In recent years, non-rigid shapes have attracted growing interest, which has led to rapid development of the field, where state-of-the-art results from very different sciences - theoretical and numerical geometry, optimization, linear algebra, graph theory, machine learning and computer graphics, to mention several - are applied to find solutions. This book gives an overview of the current state of science in analysis and synthesis of non-rigid shapes. Everyday examples are used to explain concepts and to illustrate different techniques. The presentation unfolds systematically and numerous figures enrich the engaging exposition. Practice problems follow at the end of each chapter, with detailed solutions to selected problems in the appendix. A gallery of colored images enhances the text. This book will be of interest to graduate students, researchers and professionals in different fields of mathematics, computer science and engineering. It may be used for courses in computer vision, numerical geometry and geometric modeling and computer graphics or for self-study.

The Changing Shape of Geometry

The Changing Shape of Geometry
  • Author : Mathematical Association,Mathematical Association of America
  • Publisher :Unknown
  • Release Date :2003-01-09
  • Total pages :541
  • ISBN : 0521531624
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Summary : Collection of popular articles on geometry from distinguished mathematicians and educationalists.

Shapes and Shadows

Shapes and Shadows
  • Author : Madison Julius Cawein
  • Publisher :Unknown
  • Release Date :1898
  • Total pages :77
  • ISBN : UCAL:$B798972
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Summary :

The Monctons

The Monctons
  • Author : Susanna Moodie
  • Publisher :Unknown
  • Release Date :1856
  • Total pages :303
  • ISBN : SRLF:A0001315886
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Summary :

Secrets of the Olympic Ceremonies

Secrets of the Olympic Ceremonies
  • Author : Myles Garcia
  • Publisher :Unknown
  • Release Date :2014-09-05
  • Total pages :150
  • ISBN : 9781456608088
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Summary : Everything you always wanted to know about Olympic rituals and ceremonies but were too afraid to ask. Untold stories of Olympic intrigue and chicanery woven with secrets and behind-the-scene buzz of how these multimillion-dollar spectacles are put together. It's a privileged, sneak peek into the guarded, secretive world of the making of Olympic ceremonies including: * Full histories of the various torch relays through the years * How they lit the cauldrons--from Moscow to Sydney to Beijing * Who was first with certain stunts and the production concepts you never saw * More than 150 images-many never-before-published photos and schematics-of Summer and Winter Olympic ceremonies... make SECRETS the definitive, comprehensive volume on the subject. Written by someone who's worked with at least two Olympic Games and has watched almost every Olympic ceremony since 1968. Make this your indispensible guide to the magic, wonder and spectacle of the XXXth Olympic Games which open in London on 27 July 2012.

The Geometry of Walker Manifolds

The Geometry of Walker Manifolds
  • Author : Miguel Brozos-Vázquez
  • Publisher :Unknown
  • Release Date :2009
  • Total pages :159
  • ISBN : 9781598298192
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Summary : Basic algebraic notions -- Introduction -- A historical perspective in the algebraic context -- Algebraic preliminaries -- Jordan normal form -- Indefinite geometry -- Algebraic curvature tensors -- Hermitian and para-Hermitian geometry -- The Jacobi and skew symmetric curvature operators -- Sectional, Ricci, scalar, and Weyl curvature -- Curvature decompositions -- Self-duality and anti-self-duality conditions -- Spectral geometry of the curvature operator -- Osserman and conformally Osserman models -- Osserman curvature models in signature (2, 2) -- Ivanov-Petrova curvature models -- Osserman Ivanov-Petrova curvature models -- Commuting curvature models -- Basic geometrical notions -- Introduction -- History -- Basic manifold theory -- The tangent bundle, lie bracket, and lie groups -- The cotangent bundle and symplectic geometry -- Connections, curvature, geodesics, and holonomy -- Pseudo-Riemannian geometry -- The Levi-Civita connection -- Associated natural operators -- Weyl scalar invariants -- Null distributions -- Pseudo-Riemannian holonomy -- Other geometric structures -- Pseudo-Hermitian and para-Hermitian structures -- Hyper-para-Hermitian structures -- Geometric realizations -- Homogeneous spaces, and curvature homogeneity -- Technical results in differential equations -- Walker structures -- Introduction -- Historical development -- Walker coordinates -- Examples of Walker manifolds -- Hypersurfaces with nilpotent shape operators -- Locally conformally flat metrics with nilpotent Ricci operator -- Degenerate pseudo-Riemannian homogeneous structures -- Para-Kaehler geometry -- Two-step nilpotent lie groups with degenerate center -- Conformally symmetric pseudo-Riemannian metrics -- Riemannian extensions -- The affine category -- Twisted Riemannian extensions defined by flat connections -- Modified Riemannian extensions defined by flat connections -- Nilpotent Walker manifolds -- Osserman Riemannian extensions -- Ivanov-Petrova Riemannian extensions -- Three-dimensional Lorentzian Walker manifolds -- Introduction -- History -- Three dimensional Walker geometry -- Adapted coordinates -- The Jordan normal form of the Ricci operator -- Christoffel symbols, curvature, and the Ricci tensor -- Locally symmetric Walker manifolds -- Einstein-like manifolds -- The spectral geometry of the curvature tensor -- Curvature commutativity properties -- Local geometry of Walker manifolds with -- Foliated Walker manifolds -- Contact Walker manifolds -- Strict Walker manifolds -- Three dimensional homogeneous Lorentzian manifolds -- Three dimensional lie groups and lie algebras -- Curvature homogeneous Lorentzian manifolds -- Diagonalizable Ricci operator -- Type II Ricci operator -- Four-dimensional Walker manifolds -- Introduction -- History -- Four-dimensional Walker manifolds -- Almost para-Hermitian geometry -- Isotropic almost para-Hermitian structures -- Characteristic classes -- Self-dual Walker manifolds -- The spectral geometry of the curvature tensor -- Introduction -- History -- Four-dimensional Osserman metrics -- Osserman metrics with diagonalizable Jacobi operator -- Osserman Walker type II metrics -- Osserman and Ivanov-Petrova metrics -- Riemannian extensions of affine surfaces -- Affine surfaces with skew symmetric Ricci tensor -- Affine surfaces with symmetric and degenerate Ricci tensor -- Riemannian extensions with commuting curvature operators -- Other examples with commuting curvature operators -- Hermitian geometry -- Introduction -- History -- Almost Hermitian geometry of Walker manifolds -- The proper almost Hermitian structure of a Walker manifold -- Proper almost hyper-para-Hermitian structures -- Hermitian Walker manifolds of dimension four -- Proper Hermitian Walker structures -- Locally conformally Kaehler structures -- Almost Kaehler Walker four-dimensional manifolds -- Special Walker manifolds -- Introduction -- History -- Curvature commuting conditions -- Curvature homogeneous strict Walker manifolds -- Bibliography.

The First Six Books of the Elements of Euclid

The First Six Books of the Elements of Euclid
  • Author : Oliver Byrne,Euclid
  • Publisher :Unknown
  • Release Date :1847
  • Total pages :268
  • ISBN : OXFORD:590345095
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Summary : "Byrne ... considered that it might be easier to learn geometry if colors were substituted for the letters usually used to designate the angles and lines of geometric figures. Instead of referring to, say, 'angle ABC,' Byrne's text substituted a blue or yellow or red section equivalent to similarly colored sections in the theorem's main diagram."--Friedman.

Christmas Shapes

Christmas Shapes
  • Author : Riley Weber
  • Publisher :Unknown
  • Release Date :2014-12-08
  • Total pages :34
  • ISBN : 150537121X
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Summary : This is a fun Christmas shapes book, for ages 2-6, These Christmas shapes will encourage your child to identify shapes in real life and help your child improve geometric shape recognition and fine motor skills. This Christmas shapes book is brimming with the fun of polygons and elementary geometry, and get your child excited about the shapes that surround him or her every day. Perfect for early and beginning readers! Bright and fun shapes on every page! Great for reading aloud with friends and family! Lots of Christmas fun for kids to enjoy! Fun for children ages 2-6!Riley Weber is a best-selling children's book author and illustrator. His goal is to provide quality entertainment while truly making learning fun . Riley's books reflect this. He has written over two dozen children's books as well as composed and recorded over ten full children's music albums by an artist he created; Nooshi. Merry Christmas and a Happy New Year!

Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering

Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering
  • Author : Fabio Silva Botelho
  • Publisher :Unknown
  • Release Date :2020
  • Total pages :576
  • ISBN : 0367356740
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Summary : "The book discusses the basic concepts of functional analysis, measure and integration theory, calculus of variations and duality aiming applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity by the author"--

The Geometry Code

The Geometry Code
  • Author : Bruce Rawles
  • Publisher :Unknown
  • Release Date :2012-04
  • Total pages :218
  • ISBN : 0965640574
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Summary : Integrate practical insights from modern physics, ancient Hermetic Laws, non-dual meta-physics, transpersonal psychology, and humor, as tools for undoing conflicting beliefs we've dreamed ourselves into. The seven Hermetic laws are explored in depth and demonstrate how a mindfulness that embraces 'other' as 'self' can reverse the typical misapplication of these inescapable laws of Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause & Effect and Generation. Ubiquitous geometric symbols, paired to each of these laws - the circle, vesica piscis, sine wave, line, spiral, fractal and yin-yang - and their countless commonplace variations, seen from the vantage point of shared interests, reflect these ideas. The inspired use of natural law restores attributes of life, love, strength, purity, beauty, perfection and gratitude to our awareness.

Just Chilling Adult Colouring Book

Just Chilling Adult Colouring Book
  • Author : Elaine Phillips
  • Publisher :Unknown
  • Release Date :2016-01-19
  • Total pages :36
  • ISBN : 1523489189
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Summary : Just chilling, toss away your worries for this moment and relax! Grab a marker or crayon and brighten your time with colour. Just chill and relax your brain for a couple of minutes, take a deep breath and unwind! Yes JUST CHILL!!

Yes!

Yes!
  • Author : John Fuhrman
  • Publisher :Unknown
  • Release Date :2016-06-02
  • Total pages :228
  • ISBN : 069273337X
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Summary : While everyone loves to hear "Yes," when they ask for something, too many fear that they might get a "no," instead and that fear prevents them from even trying. "YES!" gives people the opportunity to explore the risk/reward of overcoming that fear which is causing a two letter word to hold them back from their success. Read what others are saying. Glowing Comments from Business Leaders About... Yes! - How Noes Prepare You For The Yeses that Shape Your Future John Fuhrman "Enthusiasm is contagious, and "Yes!" is worth catching." -Annette Sykora, Past Chairperson, National Auto Dealers Association and owner of multiple dealerships "Say Yes to Yes! John Fuhrman's lessons and philosophies apply to an individual's pursuit of a more fulfilling life as adeptly as they do toward the pursuit of sales and marketing excellence. This is truly an inspirational read for all." -Stan Starnes, President Dent Zone Companies "John's book, Yes!, is a breath of fresh air in the world of leadership. His advice is touching and insightful, and makes me want to truly focus on mentoring others. My entire dissertation was on mentorship and this book inspired me to more effectively reach out to others in the field." -Dr. Paula Kennedy-Dudley, Director of Student Services, School of Nursing University of North Carolina at Wilmington "John has written another masterpiece in personal growth. Yes! Is a fascinating and insightful interpretation of two simple words we use every day. After reading this book, you may never look at yes or no in the same way." -Carolyn Kindley-Single Broker/Founder/Certified Mentor Green Parachute, LLC "Congratulations on a great read! You remind us of the importance of staying positive; having a great plan. I like the way you interweaved personal experiences to illustrate various points. Thank you for sharing Yes!" Michael McHugh Senior Vice President of Sales GMAC Insurance

Quantum Gravity and Spectral Geometry

Quantum Gravity and Spectral Geometry
  • Author : Giampiero Esposito,Gennaro Miele,Bruno Preziosi
  • Publisher :Unknown
  • Release Date :2002
  • Total pages :279
  • ISBN : UOM:39015054442291
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Summary :

Artdala Adult Coloring Mandala Book

Artdala Adult Coloring Mandala Book
  • Author : Yonatan Shushan,Vidal
  • Publisher :Unknown
  • Release Date :2015-11-22
  • Total pages :100
  • ISBN : 1519477112
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Summary : Colouring Mandala is not only fun, it is also a relaxing joyful artistic experience. In modern life, our mind is constantly under attack by numerous factors fights to get our attention, it starts in the moment we open our eyes and ends when we lay in bed and try to fall asleep. Mandala drawings are a meditative tool, that helps our mind and spirit be more calm and focused, together with the joy of creating art works, it's the perfect tool for body and mind to all ages. Our mandala adult coloring book includes 50 beautiful mandalas and 50 inspiring quotes, creates a calm, artistic and meditative experience for body and mind.

Applications of Representation Theory to Dynamics and Spectral Geometry

Applications of Representation Theory to Dynamics and Spectral Geometry
  • Author : Craig J. Sutton
  • Publisher :Unknown
  • Release Date :2001
  • Total pages :229
  • ISBN : UOM:39015054115483
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Summary :

3d Surface Registration Using Geometric Spectrum of Shapes

3d Surface Registration Using Geometric Spectrum of Shapes
  • Author : Hajar Hamidian
  • Publisher :Unknown
  • Release Date :2019
  • Total pages :95
  • ISBN : OCLC:1226424158
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Summary : The function is deƠ̐1ned by the integration of a smooth term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efƠ̐1ciency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. The variation of the shape is expressed using a scale function deƠ̐1ned at each vertex. Consequently, the total energy function to align the two given surfaces can be deƠ̐1ned using the linear interpolation of the scale function derivatives. Through the optimization the energy function, the scale function can be solved and the alignment is achieved. After the alignment, the eigenvectors can be employed to calculate the point to point correspondence of the surfaces. Therefore, the proposed method can accurately deƠ̐1ne the displacement of the vertices. For both methods, we evaluate them by conducting some experiments on synthetic and real data using hippocampus and heart data. These experiments demonstrate the advantages and accuracy of our methods. We then integrate our methods to a workƠ̐2ow system named DataView. Using this workƠ̐2ow system, users can design, save, run, and share their workƠ̐2ow using their web-browsers without the need of installing any software and regardless of the power of their computers. We have also integrated Grid to this system therefore the same task can be executed on up to 64 different cases which will increase the performance of the system enormously.